A Positive Definite Estimator of the Non Stationary Covariance of Random Fields

Abstract

This paper proposes a non parametric estimator of the covariance function for 2-dimensional random fields by regularization of the empirical covariance matrix by a convolution kernel. The main feature of this estimator is its positive definiteness everywhere on its domain while it does not assume stationarity of the field. We present several choices of the kernel, then we provide some insight for the selection of the smoothing parameter involved. We illustrate some of our results on a one dimensional simulated dataset and on actual 2-dimensional rainfall data.